Abstract
We present a straightforward method for the calculation of phase-matching conditions based on the angle-dependent refractive index in biaxial crystals. Considering the refractive indices relying on angular orientation of wave vector and optical axis angle, we acquire the numerical curves of phase-matching angles. We then obtain the effective nonlinear coefficient for a spontaneous parametric down conversion (SPDC) process in BiB3O6 (BIBO) crystal, and ascertain the optimal phase-matching directions for types I and II. Moreover, we focus on the angular gradient of the pump and emission wave refractive indices near the exact phase-matching direction, and compare the SPDC with the double frequency process in the geometrical relations of the refractive index ellipsoids. This method is superior in ascertaining the space distribution of pump and emission waves, and it is convenient for deciding the parameters of phase matching without solving the quadratic Fresnel equations.
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